We investigate how job displacement affects whom men marry and study implications for marriage market matching theory. Leveraging quasi-experimental variation from Danish establishment closures, we show that job displacement leads men to break up if matched with low-earning women and to re-match with higher earning women. We use a general search and matching model of the marriage market to derive several implications of our empirical findings: (i) husbands' and wives' incomes are substitutes rather than complements in the marriage market; (ii) our findings are hard to reconcile with one-dimensional matching, but are consistent with multidimensional matching; (iii) a substantial part of the cross-sectional correlation between spouses' incomes arises spuriously from sorting on unobserved characteristics. We highlight the relevance of our results by simulating how the effect of rising individual-level inequality on between-household inequality is shaped by marital sorting.